Discrete Mathematics - Vol 2 | 12. Combinatorial Proofs by Abraham | Learn Smarter
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12. Combinatorial Proofs

The chapter delves into combinatorial proofs, emphasizing the importance of counting arguments to demonstrate the equivalence of expressions rather than simplification. It illustrates concepts through simple examples and explores Pascal's identity as a significant combinatorial proof, highlighting the distinction between selecting objects and those being left out. Overall, key combinatorial concepts such as permutations and combinations are introduced, along with their formulas, discussing both cases with and without repetitions.

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Sections

  • 12

    Combinatorial Proofs

    Combinatorial proofs use counting arguments to establish the equality of two expressions without simplifying them.

    Learning Practice

  • 12.1

    Definition Of Combinatorial Proofs

    Combinatorial proofs are strategies used in combinatorics to establish the equality of two expressions by counting the same object in different ways.

    Learning Practice

  • 12.2

    Example Proof Of Equality

    This section explores combinatorial proofs, demonstrating their use in proving the equality of permutations and combinations without expanding expressions.

    Learning Practice

  • 12.3

    Pascal's Identity

    Pascal's Identity relates to combinatorial proofs, demonstrating how to equate different ways of choosing objects.

    Learning Practice

  • 12.3.1

    Category 1 Of Combinations

    This section introduces combinatorial proofs, emphasizing the counting methods used to demonstrate equalities without expanding expressions.

    Learning Practice

  • 12.3.2

    Category 2 Of Combinations

    This section introduces combinatorial proofs, explaining their significance and the process of using counting arguments to prove identities in combinatorics.

    Learning Practice

  • 12.4

    Conclusion Of The Lecture

    This section concludes the lecture with an emphasis on combinatorial proofs, their significance in combinatorics, and a recap of permutations and combinations.

    Learning Practice

References

ch34 part B.pdf

Class Notes

Memorization

What we have learnt

  • Combinatorial proofs rely o...
  • Pascal's identity illustrat...
  • The distinction between sel...

Final Test

Revision Tests